To grill radicchio and endives so that they are flavorful and moist, place them close together on the grill.
Heat grill until it is medium hot. Slice the radicchio lengthwise into six wedges. Slice the Belgian endives lengthwise into four wedges. Using a pastry brush, brush the olive oil over all sides of the radicchio and endive wedges. Sprinkle radicchio and endive wedges with salt and pepper. Place the radicchio and endive wedges on the grill, away from direct flame. Cook, turning occasionally, until golden and tender, 6 to 8 minutes depending on heat of grill. Serve immediately.